Heat oil in a large skillet or wok over medium-high heat. Add chicken and season with salt and pepper. Stir-fry about 2 minutes, until no pink remains. Add water chestnuts; stir 1 minute. Add 5 T. Sesame Ginger Sauce and heat for 2 minutes, stirring often, until bubbly. Stir in the sliced green onions; remove from heat.
Transfer chicken to a bowl. Arrange on a large platter with lettuce, fillings, and sauces. Serve fillings in purple cabbage leaves if desired.
To eat, spoon some of each ingredient into a lettuce leaf and fold like a little burrito.
6-8 appetizer portions